Identifier
Values
[1,0] => [1] => {{1}} => [1] => 0
[1,0,1,0] => [1,2] => {{1},{2}} => [1,2] => 0
[1,1,0,0] => [2,1] => {{1,2}} => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => {{1},{2},{3}} => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => {{1},{2,3}} => [1,3,2] => 1
[1,1,0,0,1,0] => [2,1,3] => {{1,2},{3}} => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => {{1,2,3}} => [2,3,1] => 1
[1,1,1,0,0,0] => [3,2,1] => {{1,3},{2}} => [3,2,1] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => {{1},{2},{3},{4}} => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => {{1},{2},{3,4}} => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => {{1},{2,3},{4}} => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => {{1},{2,3,4}} => [1,3,4,2] => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => {{1},{2,4},{3}} => [1,4,3,2] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => {{1,2},{3},{4}} => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => {{1,2},{3,4}} => [2,1,4,3] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => {{1,2,3},{4}} => [2,3,1,4] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => {{1,2,3,4}} => [2,3,4,1] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => {{1,2,4},{3}} => [2,4,3,1] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => {{1,3},{2},{4}} => [3,2,1,4] => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => {{1,3,4},{2}} => [3,2,4,1] => 2
[1,1,1,0,1,0,0,0] => [3,4,2,1] => {{1,2,3,4}} => [2,3,4,1] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => {{1,4},{2,3}} => [4,3,2,1] => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => [1,2,4,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => {{1},{2},{3,5},{4}} => [1,2,5,4,3] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => [1,3,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => [1,3,2,5,4] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => {{1},{2,3,5},{4}} => [1,3,5,4,2] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => {{1},{2,4},{3},{5}} => [1,4,3,2,5] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => {{1},{2,4,5},{3}} => [1,4,3,5,2] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => {{1},{2,5},{3,4}} => [1,5,4,3,2] => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => [2,1,3,5,4] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => [2,1,4,3,5] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => {{1,2},{3,4,5}} => [2,1,4,5,3] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => {{1,2},{3,5},{4}} => [2,1,5,4,3] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => {{1,2,3},{4,5}} => [2,3,1,5,4] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => {{1,2,3,5},{4}} => [2,3,5,4,1] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => {{1,2,4},{3},{5}} => [2,4,3,1,5] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => {{1,2,4,5},{3}} => [2,4,3,5,1] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => {{1,2,5},{3,4}} => [2,5,4,3,1] => 3
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => {{1,3},{2},{4},{5}} => [3,2,1,4,5] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => {{1,3},{2},{4,5}} => [3,2,1,5,4] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => {{1,3,4},{2},{5}} => [3,2,4,1,5] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => {{1,3,4,5},{2}} => [3,2,4,5,1] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => {{1,3,5},{2},{4}} => [3,2,5,4,1] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => {{1,3,5},{2,4}} => [3,4,5,2,1] => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => {{1,4},{2,3},{5}} => [4,3,2,1,5] => 3
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => {{1,4,5},{2,3}} => [4,3,2,5,1] => 3
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => {{1,2,4,5},{3}} => [2,4,3,5,1] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => {{1,5},{2,4},{3}} => [5,4,3,2,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => {{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => {{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => {{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => {{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => {{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 1
>>> Load all 637 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => {{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => {{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => {{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => {{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => {{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => {{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => {{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => {{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => {{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => {{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => {{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => {{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => {{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => {{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => {{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => {{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => {{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => {{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => {{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => {{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => {{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => {{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => {{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => {{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => {{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => {{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => {{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => {{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => {{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => {{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => {{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => {{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => {{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => {{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => {{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => {{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => {{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => {{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => {{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => {{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => {{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => {{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => {{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => {{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => {{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => {{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => {{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => {{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => {{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => {{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => {{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => {{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => {{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => {{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => {{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => {{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => {{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => {{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => {{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => {{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => {{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => {{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => {{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => {{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => {{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => {{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => {{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => {{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => {{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => {{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => {{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => {{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => {{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => {{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => {{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => {{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => {{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => {{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => {{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => {{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => {{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => {{1,3,5,6,7},{2,4}} => [3,4,5,2,6,7,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => {{1,3,6},{2,5},{4},{7}} => [3,5,6,4,2,1,7] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => {{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => {{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => {{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => {{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}} => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}} => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => {{1},{2,3,5,8},{4,7},{6}} => [1,3,5,7,8,6,4,2] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => {{1},{2,4},{3},{5,7},{6},{8}} => [1,4,3,2,7,6,5,8] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => {{1},{2,4,6,8},{3},{5},{7}} => [1,4,3,6,5,8,7,2] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => {{1},{2,4,8},{3},{5,7},{6}} => [1,4,3,8,7,6,5,2] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => {{1},{2,6,8},{3,5},{4},{7}} => [1,6,5,4,3,8,7,2] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => {{1},{2,8},{3,7},{4,6},{5}} => [1,8,7,6,5,4,3,2] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,3,4,5,6,7,8] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => {{1,2},{3,4},{5,6,8},{7}} => [2,1,4,3,6,8,7,5] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => {{1,2},{3,4},{5,7,8},{6}} => [2,1,4,3,7,6,8,5] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}} => [2,1,4,3,8,7,6,5] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => {{1,2},{3,4,6},{5},{7,8}} => [2,1,4,6,5,3,8,7] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => {{1,2},{3,5,6},{4},{7,8}} => [2,1,5,4,6,3,8,7] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => {{1,2},{3,5,7,8},{4},{6}} => [2,1,5,4,7,6,8,3] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}} => [2,1,6,5,4,3,8,7] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => {{1,2},{3,8},{4,7},{5,6}} => [2,1,8,7,6,5,4,3] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => {{1,2,3,5,8},{4,6,7}} => [2,3,5,6,8,7,4,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}} => [2,4,3,1,6,5,8,7] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => {{1,2,4},{3},{5,6,8},{7}} => [2,4,3,1,6,8,7,5] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => {{1,2,4},{3},{5,7,8},{6}} => [2,4,3,1,7,6,8,5] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}} => [3,2,1,4,5,6,7,8] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}} => [3,2,1,4,5,8,7,6] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => {{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,6,5,8,7,4] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => {{1,3},{2},{4,8},{5,7},{6}} => [3,2,1,8,7,6,5,4] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}} => [3,2,4,1,6,5,8,7] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => {{1,3,4},{2},{5,6,8},{7}} => [3,2,4,1,6,8,7,5] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => {{1,3,4},{2},{5,7,8},{6}} => [3,2,4,1,7,6,8,5] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => {{1,3,5},{2},{4},{6,8},{7}} => [3,2,5,4,1,8,7,6] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => {{1,3,5,6},{2},{4},{7,8}} => [3,2,5,4,6,1,8,7] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => {{1,3,5,7},{2},{4},{6},{8}} => [3,2,5,4,7,6,1,8] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => {{1,3,5,7,8},{2},{4},{6}} => [3,2,5,4,7,6,8,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => {{1,3,6,8},{2},{4,5},{7}} => [3,2,6,5,4,8,7,1] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => {{1,3,7},{2},{4,6},{5},{8}} => [3,2,7,6,5,4,1,8] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => {{1,3,5,6,7,8},{2,4}} => [3,4,5,2,6,7,8,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => {{1,3,5,6,7,8},{2,4}} => [3,4,5,2,6,7,8,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => {{1,3,8},{2,4,5,6,7}} => [3,4,8,5,6,7,2,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}} => [4,3,2,1,5,6,7,8] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}} => [4,3,2,1,6,5,8,7] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}} => [4,3,2,1,8,7,6,5] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}} => [4,3,2,5,6,7,8,1] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => {{1,4,5,6,7,8},{2,3}} => [4,3,2,5,6,7,8,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => {{1,4,5,6,7,8},{2,3}} => [4,3,2,5,6,7,8,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => {{1,4,5,6,7,8},{2,3}} => [4,3,2,5,6,7,8,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => {{1,4,5,7,8},{2,3,6}} => [4,3,6,5,7,2,8,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => {{1,4,5,8},{2,3,6,7}} => [4,3,6,5,8,7,2,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => {{1,3,4,5,7,8},{2,6}} => [3,6,4,5,7,2,8,1] => 3
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => {{1,3,4,5,7,8},{2,6}} => [3,6,4,5,7,2,8,1] => 3
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => {{1,4,5,8},{2,3,6,7}} => [4,3,6,5,8,7,2,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => {{1,5},{2,4},{3},{6},{7},{8}} => [5,4,3,2,1,6,7,8] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => {{1,5},{2,4},{3},{6,8},{7}} => [5,4,3,2,1,8,7,6] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => {{1,5,7},{2,4},{3},{6},{8}} => [5,4,3,2,7,6,1,8] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => {{1,4,5,8},{2,3,6,7}} => [4,3,6,5,8,7,2,1] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => {{1,6},{2,5},{3,4},{7,8}} => [6,5,4,3,2,1,8,7] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => {{1,7},{2,6},{3,5},{4},{8}} => [7,6,5,4,3,2,1,8] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => {{1,7,8},{2,6},{3,5},{4}} => [7,6,5,4,3,2,8,1] => 6
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}} => [8,7,6,5,4,3,2,1] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => {{1,9},{2,8},{3,7},{4,6},{5},{10}} => [9,8,7,6,5,4,3,2,1,10] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => {{1},{2,10},{3,9},{4,8},{5,7},{6}} => [1,10,9,8,7,6,5,4,3,2] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,9,8,7,6,4,3,2,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,5,7,8,4,3,2,1,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,7,8,6,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,5,7,9,8,6,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,8,7,9,6,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,4,6,7,5,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,5,6,4,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,6,5,7,8,9,4,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => {{1,3,4,5,6,7,8,9},{2}} => [3,2,4,5,6,7,8,9,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,9,5,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,3,7,8,9,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,7,3,9,8,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,9,8,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,7,9,8,6,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,6,8,5,9,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => {{1,3,4,5,6,7,8,9,10},{2}} => [3,2,4,5,6,7,8,9,10,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,2,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => [3,2,1,4,5,6,7,8,9] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => {{1,4},{2,3},{5},{6},{7},{8},{9}} => [4,3,2,1,5,6,7,8,9] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,3,4,5,6,7,8,9,10] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => [2,1,4,3,6,5,8,7,10,9] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [3,2,1,4,5,6,7,8,9,10] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,8,10,9,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => [2,1,3,4,5,6,7,8,9,10,11] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,4,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,6,9,8,10,7,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,8,7,9,6,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,8,7,9,2,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,4,6,3,8,7,9,2,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,7,6,8,5,9,2,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,7,6,8,3,9,2,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,10,9,2,1] => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => 1
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Description
The staircase size of the code of a permutation.
The code $c(\pi)$ of a permutation $\pi$ of length $n$ is given by the sequence $(c_1,\ldots,c_{n})$ with $c_i = |\{j > i : \pi(j) < \pi(i)\}|$. This is a bijection between permutations and all sequences $(c_1,\ldots,c_n)$ with $0 \leq c_i \leq n-i$.
The staircase size of the code is the maximal $k$ such that there exists a subsequence $(c_{i_k},\ldots,c_{i_1})$ of $c(\pi)$ with $c_{i_j} \geq j$.
This statistic is mapped through Mp00062Lehmer-code to major-code bijection to the number of descents, showing that together with the number of inversions St000018The number of inversions of a permutation. it is Euler-Mahonian.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].